is √70 Rational or Irrational?

Answer 1

√70 is also √2 x √5 x √7
2, 5, 7 are prime number.
and it happens that √2, for instance, is irrational, as you cannot find two numbers 'a' and 'b' that will be such as √2=a/b

So √70 is also irrational

Answer 2

You're really asking if the polynomial f(x)=x^2-70 has a rational root. By the rational root test, the only possible roots are the divisors of 70: 1,2,5,7,10,14,35, and 70, and their negatives. Check that none of these work. So f does not have a rational root, thus √70 is irrational.

Answer 3

√70 is an irrational because, numbers that cannot be written as the division of one integer by another are termed irrational. Or it is not possible to find two integers that represent this number if one of the integers is divided by the other. For example 22/7 is not exactly equal to π.

Answer 4

Suppose it is rational, than there are two integers m,n having no common divisors for which m^2/n^2 = 70.

m^2 must be divisible by 70, or in 2,5 and 7.

therefore 2,5,7 must divide m, and thus 4,25 and 49 divide m^2.
Which implies that m^2 is divisible by 4900, and therefore n^2 must be divisible by 70, which means that n is divisible by 70, and this is a contradiction to our assumption that m and n have no common divisors.

QED

Answer 5

It is rational (by the way, a rational number is a number that can be expressed as an integer or fraction). Here is how you figure it out:

√70=8.3666002
Now you must convert that into a fraction.
As a fraction, 8.3666002 is (41833001)/(5000000).

Answer 6

irrational but not trancedent

Answer 7

irrational

Answer 8

irrational

Answer 9

irrational......

Answer 10

irrational
its a repeating decimal